Most browsers support cookies of up to 4096 bytes. That is plenty of space for storing a few values on the user's computers, but you would not want to try to store a dataset or some other potentially large piece of data in a cookie. More practically, you probably do not want to store a big collection of user information in a cookie. Instead, you would want to store a user number or other identifier. Then, when the user visits your site again, you would use the user ID to look up user details in a database. (But see Cookies and Security for some caveats about storing user information.)
Browsers also impose limitations on how many cookies your site can store on the user's computer. Most browsers allow only 20 cookies per site; if you try to store more, the oldest cookies are discarded. Some browsers also put an absolute limit, usually 300, on the number of cookies they will accept from all sites combined.